http://iscoresports.com/

Does iscore keep catcher stats whether the game is entered live or when the game stats are entered manually after the fact from the paper scorebook?

Are you looking for particular stats? iscore does keep some catcher specific stats such as passed balls, steal attempts, caught stealing, etc. How you score the game (live vs paper transfer) does not matter if you are entering the entire game. Stats can also be overrode if you ae entering later and just want to keep track of stats without having to enter the entire game.